Find Least Common Multiple of 27, 64 and 105 using division method..

Answer

LCM( 27, 64, 105 ) = 60480

Explanation

Step 1 : Write the given numbers in a horizontal line.

105

Step 2 : Divide the given numbers by smallest prime number. In this example we can divide by 2.

(if any number is not divisible by 2, write it down unchanged)

2	27	64	105
	27	32	105

Step 3 : Continue dividing by prime numbers till we get 1 in all columns.

2	27	64	105
2	27	32	105
2	27	16	105
2	27	8	105
2	27	4	105
2	27	2	105
3	27	1	105
3	9	1	35
3	3	1	35
5	1	1	35
7	1	1	7
	1	1	1

Step 4 : Multiply numbers in first column to get LCM.

LCM( 27, 64, 105 ) = 2 · 2 · 2 · 2 · 2 · 2 · 3 · 3 · 3 · 5 · 7 = 60480 .

This solution can be visualized using a Venn diagram.

The LCM is equal to the product of all the numbers on the diagram.

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2	27	64	105
2	27	32	105
2	27	16	105
2	27	8	105
2	27	4	105
2	27	2	105
3	27	1	105
3	9	1	35
3	3	1	35
5	1	1	35
7	1	1	7
	1	1	1

2	27	64	105
2	27	32	105
2	27	16	105
2	27	8	105
2	27	4	105
2	27	2	105
3	27	1	105
3	9	1	35
3	3	1	35
5	1	1	35
7	1	1	7
	1	1	1

2	27	64	105
2	27	32	105
2	27	16	105
2	27	8	105
2	27	4	105
2	27	2	105
3	27	1	105
3	9	1	35
3	3	1	35
5	1	1	35
7	1	1	7
	1	1	1